A Lucas–Lehmer approach to generalised Lebesgue–Ramanujan–Nagell equations

Vandita Patel
2021 The Ramanujan journal  
AbstractWe describe a computationally efficient approach to resolving equations of the form $$C_1x^2 + C_2 = y^n$$ C 1 x 2 + C 2 = y n in coprime integers, for fixed values of $$C_1$$ C 1 , $$C_2$$ C 2 subject to further conditions. We make use of a factorisation argument and the Primitive Divisor Theorem due to Bilu, Hanrot and Voutier.
doi:10.1007/s11139-021-00408-9 fatcat:nhyu3e4nvzhcxkud2ah7ubcqne